Linear Equations in Real-World Scenarios Quick Check

Question

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Question
An ice cream shop makes vanilla and chocolate ice cream. The vanilla ice cream machine has a 180-cup capacity, and it sells 20 cups per day. The chocolate ice cream machine has a 140-cup capacity, and it sells 16 cups per day. Write and solve an equation to show when the two machines will have the same amount of ice cream left.(1 point)
Responses

180+16x=140+20x
; x=−10
180 plus 16 x equals 140 plus 20 x ; x equals negative 10

180−20x=140−16x
; x=20
180 minus 20 x equals 140 minus 16 x ; x equals 20

180−20x=140−16x
; x=10
180 minus 20 x equals 140 minus 16 x ; x equals 10

140+16x=180+20x
; x=10

Answer 1

To determine when the two machines will have the same amount of ice cream left, we can set up the equations based on the information provided.

Let \( x \) be the number of days that pass.

• For the vanilla ice cream machine, which starts with 180 cups and sells 20 cups per day, the amount left after \( x \) days is: \[ 180 - 20x \]

• For the chocolate ice cream machine, which starts with 140 cups and sells 16 cups per day, the amount left after \( x \) days is: \[ 140 - 16x \]

To find when they will have the same amount of ice cream left, we can set the two equations equal to each other: \[ 180 - 20x = 140 - 16x \]

Now, we can solve for \( x \):

1. Rearranging the equation: \[ 180 - 140 = 20x - 16x \] \[ 40 = 4x \]

2. Dividing both sides by 4: \[ x = 10 \]

So, in 10 days, both machines will have the same amount of ice cream left.

The correct response is: 180−20x=140−16x ; x=10